题  目：Towards Convexity in Anomaly Detection: A New Formulation of SSLM with Unique Optimal Solutions

主讲人：王浩

单   位：上海科技大学

时   间：2025年10月31日 14:45

地   点 ：郑州校区九章学堂南楼C座209

摘  要：An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner similar to SVMs and limits their applicability in large-scale scenarios. In this paper, we introduce a novel convex SSLM formulation which has been demonstrated to revert to a convex quadratic programming problem for hyperparameter values of interest. Leveraging the convexity of our method, we derive numerous results that are unattainable with traditional nonconvex approaches. We conduct a thorough analysis of how hyperparameters influence the optimal solution, pointing out scenarios where optimal solutions can be trivially found and identifying instances of ill-posedness. Most notably, we establish connections between our method and traditional approaches, providing a clear determination of when the optimal solution is unique—a task unachievable with traditional nonconvex methods. We also derive the ν-property to elucidate the interactions between hyperparameters and the fractions of support vectors and margin errors in both positive and negative classes.

简   介：王浩博士于2015年5月在美国Lehigh University工业工程系获得博士学位，导师为Frank E. Curtis，并于2010年和2007年在北京航空航天大学数学与应用数学系分别获得理学硕士和学士学位。王浩博士于2016年3月加入上海科技大学信息与技术学院。当前研究领域主要为稀疏正则、低秩填充、非线性优化等问题。